Finite-time event-triggered output-feedback adaptive decentralized echo-state network fault-tolerant control for interconnected pure-feedback nonlinear systems with input saturation and external disturbances: A fuzzy control-error approach

In this paper, we introduce a decentralized Event-Triggered fault-tolerant echo-state network (ESN) direct adaptive controller for uncertain interconnected nonlinear systems in pure-feedback form. The proposed controller addresses input saturation, actuator faults, external disturbances, and unavailable states for measurement. Unlike the existing works in the literature that adapts the ESN weights using the tracking error, our method employs the control error that is estimated using a fuzzy inference system, to derive the adaptation laws. The complexity explosion typically seen with recursive back-stepping and Dynamic Surface Control (DSC) designs is completely avoided. Our control scheme addresses four types of state-dependent actuator faults: bias, drift, loss of accuracy, as well as loss of effectiveness. The ESNs approximate unknown ideal control laws, while robust terms are added to enhance the stability of the closed-loop system. Stability analysis ensures that tracking errors converge, in finite time, to a small compact set near the origin due to the strictly positive real (SPR) property. Simulation results of a quadrotor UAV and a mathematical system are presented. A comparative analysis is performed with another approach to emphasize the effectiveness of the proposed method.